Method and apparatus for block-wise decision-feedback equalization for wireless communication

ABSTRACT

Techniques for performing decision feedback equalization are described. A feed-forward filter response and a feedback filter response are derived based on a channel estimate and a reliability parameter and further without constraint on the feedback filter response or with a constraint of no feedback for an on-time sample. The reliability parameter is indicative of the reliability of the feedback used for equalization and may be frequency dependent or frequency invariant. Different feed-forward and feedback filter responses may be derived with different constraints on the feedback filter and different assumptions for the reliability parameter. Equalization is performed with the feed-forward and feedback filter responses. If equalization is performed for multiple iterations then, for each iteration, the reliability parameter may be updated, the feed-forward and feedback filter responses may be derived based on the updated reliability parameter, and equalization may be performed with the filter responses for the iteration.

CLAIM OF PRIORITY UNDER 35 U.S.C. §119 AND 35 U.S.C. §120

The present application for patent is a continuation and claims priorityto patent application Ser. No. 11/392,306 filed Mar. 28, 2006 and claimspriority to Provisional Application Ser. No. 60/666,334, and ProvisionalApplication Ser. No. 60/666,416, both filed Mar. 29, 2005, assigned tothe assignee hereof, and expressly incorporated herein by reference.

BACKGROUND

1. Field

The present disclosure relates generally to communication, and morespecifically to techniques for performing equalization in acommunication system.

2. Background

In a communication system, a transmitter typically processes (e.g.,encodes, interleaves, symbol maps, spreads, and scrambles) traffic datato generate a sequence of chips. The transmitter then processes the chipsequence to generate a radio frequency (RF) signal and transmits the RFsignal via a communication channel. The communication channel distortsthe RF signal with a channel response and further degrades the RF signalwith noise and interference from other transmitters.

A receiver receives the transmitted RF signal and processes the receivedRF signal to obtain samples. The receiver may perform equalization onthe samples to obtain estimates of the chips sent by the transmitter.The receiver then processes (e.g., descrambles, despreads, demodulates,deinterleaves, and decodes) the chip estimates to obtain decoded data.The equalization typically has a large impact on the quality of the chipestimates as well as the overall performance.

There is therefore a need in the art for techniques to performequalization in a manner to achieve good performance.

SUMMARY

According to an embodiment of the invention, an apparatus is describedwhich includes at least one processor and a memory. The processor(s)derive a feed-forward filter response and a feedback filter responsebased on a channel estimate and a reliability parameter and furtherwithout constraint on the feedback filter response or with a constraintof no feedback for an on-time sample. The reliability parameter isindicative of the reliability of the feedback used for equalization andmay be frequency dependent or frequency invariant. The processor(s)perform equalization with the feed-forward and feedback filterresponses.

According to another embodiment, a method is provided in which afeed-forward filter response and a feedback filter response are derivedbased on a channel estimate and a reliability parameter and furtherwithout constraint on the feedback filter response or with a constraintof no feedback for an on-time sample. Equalization is performed with thefeed-forward and feedback filter responses.

According to yet another embodiment, an apparatus is described whichincludes means for deriving a feed-forward filter response and afeedback filter response based on a channel estimate and a reliabilityparameter and further without constraint on the feedback filter responseor with a constraint of no feedback for an on-time sample. The apparatusfurther includes means for performing equalization with the feed-forwardand feedback filter responses.

According to yet another embodiment, an apparatus is described whichincludes at least one processor and a memory. The processor(s) derivemultiple feed-forward filter responses for multiple signal copies basedon channel estimates for the multiple signal copies and a reliabilityparameter. The multiple signal copies may be obtained from over-samplingand/or multiple receive antennas. The processor(s) also derive afeedback filter response based on the channel estimates and thereliability parameter. The processor(s) perform equalization on inputsymbols for the multiple signal copies with the multiple feed-forwardfilter responses and the feedback filter response.

According to yet another embodiment, a method is provided in whichmultiple feed-forward filter responses for multiple signal copies arederived based on channel estimates for the multiple signal copies and areliability parameter. A feedback filter response is derived based onthe channel estimates and the reliability parameter. Equalization isperformed on input symbols for the multiple signal copies with themultiple feed-forward filter responses and the feedback filter response.

According to yet another embodiment, an apparatus is described whichincludes means for deriving multiple feed-forward filter responses formultiple signal copies based on channel estimates for the multiplesignal copies and a reliability parameter, means for deriving a feedbackfilter response based on the channel estimates and the reliabilityparameter, and means for performing equalization on input symbols forthe multiple signal copies with the multiple feed-forward filterresponses and the feedback filter response.

According to yet another embodiment, an apparatus is described whichincludes at least one processor and a memory. The processor(s) estimatea reliability parameter based on a first data block that is decodedcorrectly, derive a feed-forward filter response and a feedback filterresponse based on a channel estimate and the reliability parameter, andperform equalization for a second data block with the feed-forward andfeedback filter responses.

According to yet another embodiment, a method is provided in which areliability parameter is estimated based on a first data block that isdecoded correctly. A feed-forward filter response and a feedback filterresponse are derived based on a channel estimate and the reliabilityparameter. Equalization is performed for a second data block with thefeed-forward and feedback filter responses.

According to yet another embodiment, an apparatus is described whichincludes means for estimating a reliability parameter based on a firstdata block that is decoded correctly, means for deriving a feed-forwardfilter response and a feedback filter response based on a channelestimate and the reliability parameter, and means for performingequalization for a second data block with the feed-forward and feedbackfilter responses.

Various aspects and embodiments of the invention are described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a time-domain model of a communication channel.

FIG. 1B shows a frequency-domain model of a communication channel.

FIG. 2A shows a chip-spaced DFE with a time-domain feedback filter.

FIG. 2B shows a chip-spaced DFE with a frequency-domain feedback filter.

FIG. 3 shows a frequency-domain model for a chip-space DFE.

FIG. 4 shows a process to derive feed-forward and feedback filterresponses.

FIG. 5 shows a process to perform decision feedback equalization.

FIG. 6A shows a fractionally-spaced DFE with a time-domain feedbackfilter.

FIG. 6B shows a fractionally-spaced DFE with a frequency-domain feedbackfilter.

FIG. 7 shows a frequency-domain model for a fractionally-spaced DFE.

FIG. 8 shows a process to derive feed-forward and feedback filterresponses.

FIG. 9 shows a process to perform equalization for multiple signalcopies.

FIG. 10 shows a process to perform decision feedback equalization basedon a reliability parameter derived from correctly decoded data blocks.

FIG. 11 shows a block diagram of a transmitter and a receiver.

DETAILED DESCRIPTION

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments.

For clarity, the following nomenclature is used in much of thedescription below. Time-domain scalars are denoted by lower case textwith index n for sample period, e.g., h(n). Frequency-domain scalars aredenoted by upper case text with index k for frequency bin, e.g., H(k).Time-domain vectors are denoted by bolded lower case cursive text, e.g.,

. Time-domain matrices are denoted by bolded upper case cursive text,e.g.,

. Frequency-domain vectors are denoted by bolded lower case regulartext, e.g., h. Frequency-domain matrices are denoted by bolded uppercase regular text, e.g., H. The terms “chips” and “samples” generallyrefer to time-domain quantities, and the term “symbols” generally refersto frequency-domain quantities.

1. Chip-Spaced DFE

FIG. 1A shows a time-domain model 100 of a communication system with atransmitter 110 and a receiver 150. Model 100 assumes that the receivedsignal is sampled at chip rate so that the sample rate is equal to thechip rate. Transmitter 110 processes traffic data and generates transmitchips s(n), which are sent via a communication channel 120. Channel 120is modeled with a time-domain impulse response of h(n) in block 124 andadditive noise of n(n) via a summer 126. The channel impulse responseh(n) includes the effects of the pulse shaping filter at transmitter110, the propagation channel, the front-end filter at receiver 150, andso on. Receiver 150 obtains input samples r(n) via channel 120 andperforms equalization on the input samples to obtain chip estimatesŝ(n), which are estimates of the transmit chips s(n).

FIG. 1B shows a frequency-domain model 102 of the communication systemin FIG. 1A. Frequency-domain model 102 is equivalent to time-domainmodel 100. The transmit chips s(n) from transmitter 110 are sent via acommunication channel 130. For channel 130, the time-domain transmitchips s(n) are transformed to the frequency domain with a K-point fastFourier transform (FFT) or a K-point discrete Fourier transform (DFT) bya unit 132 to obtain frequency-domain transmit symbols S(k). Channel 130is modeled with a channel frequency response of H(k) in block 134 andadditive noise of N(k) via a summer 136. A unit 138 performs a K-pointFFT/DFT on the time-domain noise n(n) and provides the frequency-domainnoise N(k). A unit 140 performs a K-point inverse FFT (IFFT) or aK-point inverse DFT (IDFT) on the frequency-domain input symbols R(k)from summer 136 and provides the time-domain input samples r(n) toreceiver 150.

The time-domain input samples r(n) and the frequency-domain inputsymbols R(k) may be expressed as:

r(n)=h(n)

s(n)+n(n), and  Eq (1)

R(k)=H(k)·S(k)+N(k),  Eq (2)

where

denotes a convolution.

Receiver 150 may process the input samples on a block-by-block basis. Adata block may also be called a packet, a frame, and so on. In anembodiment, each data block contains K input samples. The input samplesand input symbols may be expressed in matrix form for one data block, asfollows:

s=W _(K) ·s,  Eq (3)

r=H·s+n , and  Eq (4)

r=W _(K) ⁻¹ ·r  Eq (5)

where

-   -   s=[s(1) s(2) . . . s(K)]^(T) is a K×1 vector of transmit chips,    -   s=[S(1) S(2) . . . S(K)]^(T) is a K×1 vector of transmit        symbols,    -   r=[R(1) R(2) . . . R(K)]^(T) is a K×1 vector of received        symbols,    -   r=[r(1) r(2) . . . r(K)]^(T) is a K×1 vector of received        samples,    -   n=[N(1) N(2) . . . N(K)]^(T) is a K×1 vector of noise,    -   H is a K×K channel response matrix containing channel gains H(1)        through H(K) along the diagonal and zeros elsewhere,    -   W _(K) is a K×K Fourier matrix,    -   W _(K) ⁻¹ is a K×K inverse Fourier matrix, and    -   “^(T)” denotes a transpose.

The noise may be assumed to be additive white Gaussian noise (AWGN) withzero mean and a covariance matrix of N_(t)·I, where N_(t) is thevariance of the noise and I is the identity matrix.

The element in row k and column n of W _(K) may be given as:

W(k,n)=e ^(−j2π·(k−1)(n−1)/K).  Eq (6)

In equation (6), the “−1” is due to indices k and n starting with 1instead of 0.

Receiver 150 may perform decision feedback equalization on each block ofinput samples. A decision feedback equalizer (DFE) typically includes afeed-forward filter and a feedback filter. In an embodiment, thefeed-forward filter is implemented in the frequency domain, and thefeedback filter may be implemented in either the time domain or thefrequency domain.

FIG. 2A shows a block diagram of a model 200 with a DFE having atime-domain feedback filter. A transmitter 210 generates transmit chipss(n), which are sent via a communication channel 220. Channel 220 ismodeled with a channel impulse response of h(n) in block 224 andadditive noise of n(n) via a summer 226. A receiver 250 a obtains inputsamples r(n) via channel 220. Within receiver 250 a, an FFT/DFT unit 252transforms the input samples to the frequency domain and provides inputsymbols R(k). A feed-forward filter 260 filters the input symbols andprovides filtered symbols X(k). An IFFT/IDFT unit 264 transforms thefiltered symbols to the time domain and provides filtered samples x(n).A summer 266 subtracts feedback samples y(n) from the filtered samplesx(n) and provides equalized samples z(n). A slicer 270 slices orquantizes the equalized samples z(n) and provides chip estimates ŝ(n). Afeedback filter 272 filters the chip estimates and provides the feedbacksamples y(n).

FIG. 2B shows a block diagram of a model 202 with a DFE having afrequency-domain feedback filter. Transmitter 210 and communicationchannel 220 are as described above for FIG. 2A. A receiver 250 b obtainsinput samples r(n) via channel 220. Within receiver 250 b, FFT/DFT unit252 and feed-forward filter 260 operate on the input samples asdescribed above for FIG. 2A and provide filtered symbols X(k). Summer266 subtracts feedback symbols Y(k) from the filtered symbols X(k) andprovides equalized symbols Z(k). An IFFT/IDFT unit 268 transforms theequalized symbols to the time domain and provides equalized samplesz(n). Slicer 270 slices the equalized samples z(n) and provides chipestimates ŝ(n). An FFT/DFT unit 274 transforms the chip estimates ŝ(n)to the frequency domain and provides symbol estimates Ŝ(k). A feedbackfilter 280 filters the symbol estimates and provides the feedbacksymbols Y(k).

If a transmitted block has either a cyclic prefix or zero padding, thena linear convolution of the input samples and the impulse response of atime-domain feed-forward filter is equivalent to a cyclic convolution.In this case, the time-domain feed-forward filter may be represented inthe frequency domain by a block-wise feed-forward filter having afrequency response denoted by a K×K diagonal matrix F. Matrix F containsK filter coefficients along the diagonal for the K frequency bins andzeros elsewhere.

A time-domain feedback filter may have an impulse response denoted by anL×1 vector

=[b₀ b₁ b₂ . . . b_(L−1)]^(T). If the transmitted block has either acyclic prefix or zero padding, then the feedback samples may beexpressed as:

y =

·{circumflex over ( s )},  Eq (7)

where

-   -   {circumflex over (s)}=[ŝ(1) ŝ(2) . . . ŝ(K)]^(T) is a K×1 vector        of chip estimates,    -   y=[y(1) y(2) . . . y(K)]^(T) is a K×1 vector of feedback        samples, and

$\underset{\_}{\mathcal{B}} = \begin{bmatrix}b_{0} & 0 & \ldots & 0 & b_{L - 1} & \ldots & b_{2} & b_{1} \\b_{1} & b_{0} & \ldots & 0 & 0 & b_{L - 1} & \ldots & b_{2} \\\ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots & \ddots \\0 & \ldots & 0 & b_{L - 1} & \ldots & b_{2} & b_{1} & b_{0}\end{bmatrix}$

-   -    is a K×K circular matrix.        The circular matrix        contains elements of the impulse response vector        .

The time-domain feedback filter may be represented in the frequencydomain by a block-wise feedback filter having a frequency responsedenoted by a K×K diagonal matrix B. Matrix B contains K filtercoefficients along the diagonal for the K frequency bins and zeroselsewhere. Since

is a circular matrix,

may be diagonalized as follows:

= W _(K) ⁻¹ ·B·W _(K).  Eq (8)

FIG. 3 shows a frequency-domain model 300 with a chip-space DFE. Model300 is equivalent to model 200 in FIG. 2A and model 202 in FIG. 2B. Atransmitter 310 generates time-domain transmit chips s(n), which aresent via a communication channel 330. Channel 330 is modeled with anFFT/DFT unit 332 that transforms the transmit chips to transmit symbolsS(k), a block 334 for the channel frequency response H(k), an FFT/DFTunit 338 that transforms time-domain noise n(n) to frequency-domainnoise N(k), and a summer 336 that sums the outputs of blocks 334 and 338and provides input symbols R(k) to a receiver 350.

Within receiver 350, a feed-forward filter 360 filters the input symbolsR(k) and provides filtered symbols X(k). A summer 366 subtracts feedbacksymbols Y(k) from the filtered symbols X(k) and provides equalizedsymbols Z(k). An IFFT/IDFT unit 368 transforms the equalized symbolsZ(k) to the time domain and provides equalized samples z(n). A slicer370 slices the equalized samples z(n) and provides chip estimates ŝ(n).An FFT/DFT unit 374 transforms the chip estimates to the frequencydomain and provides symbol estimates Ŝ(k). A feedback filter 380 filtersthe symbol estimates and provides the feedback symbols Y(k).

The filtered symbols from feed-forward filter 360 may be expressed as:

$\begin{matrix}\begin{matrix}{{\underset{\_}{x} = {\underset{\_}{F} \cdot \underset{\_}{r}}},} \\{{= {{\underset{\_}{F} \cdot \underset{\_}{H} \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{s}} + {\underset{\_}{F} \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{n}}}},}\end{matrix} & {{Eq}\mspace{14mu} (9)}\end{matrix}$

where x=[X(1) X(2) . . . X(K)]^(T) is a K×1 vector of filtered symbols.

The feedback symbols from feedback filter 380 may be expressed as:

y=B−W _(K) ·{circumflex over (s)},  Eq (10)

where y=[Y(1) Y(2) . . . Y(K)]^(T) is a K×1 vector of feedback symbols.

The equalized samples provided to slicer 370 may be expressed as:

$\begin{matrix}\begin{matrix}{{\underset{\_}{z} = {{\underset{\_}{W}}_{K}^{- 1} \cdot ( {\underset{\_}{x} - \underset{\_}{y}} )}},} \\{{= {{{\underset{\_}{W}}_{K}^{- 1} \cdot ( {{\underset{\_}{F} \cdot \underset{\_}{H} \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{s}} - {\underset{\_}{B} \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{\hat{s}}}} )} + {{\underset{\_}{W}}_{K}^{- 1} \cdot \underset{\_}{F} \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{n}}}},}\end{matrix} & {{Eq}\mspace{14mu} (11)}\end{matrix}$

where z=[z(1) z(2) . . . z(K)]^(T) is a K×1 vector of equalized samples.

The feed-forward filter frequency response F and the feedback filterfrequency response B may be derived in various manners. In anembodiment, the filter responses F and B are derived based on a minimummean square error (MMSE) criterion that minimizes the mean square error(MSE) between the transmit chips s and the equalized samples z. The MSEmay be expressed as:

$\begin{matrix}\begin{matrix}{{{MSE} = {E\{ {( {z - s} )^{H} \cdot ( {z - s} )} \}}},} \\{= {{{Trace}( {E\{ {( {z - s} ) \cdot ( {z - s} )^{H}} \}} )}.}}\end{matrix} & {{Eq}\mspace{14mu} (12)}\end{matrix}$

The following assumptions may be made:

E{s·s ^(H) }=E{{circumflex over (s)}·{circumflex over (s)} ^(H) }=E _(s)·I, and  Eq (13)

E{s·{circumflex over (s)} ^(H) }=E{W _(K) ·s·ŝ ^(H) ·W _(K) }=E _(s)·R,  Eq (14)

where

-   -   E_(s) is the energy-per-chip for the transmit chips s(n),    -   E{ } denotes an expectation operation,    -   {circumflex over (s)}=[Ŝ(1) Ŝ(2) . . . Ŝ(K)]^(T) is a K×1 vector        of symbol estimates,    -   R is a K×K feedback correlation matrix, and    -   “^(H)” denotes a conjugate transpose.

Equation (13) indicates that the transmit chips s as well as the chipestimates ŝ are uncorrelated. Equation (14) describes the correlationbetween the transmit chips s and the chip estimates {circumflex over(s)}. This correlation is related to the reliability of the decisionfeedback for the DFE.

Equation (12) may be expanded and combined with equations (11), (13) and(14). The MSE may then be expressed as:

$\begin{matrix}{{{MSE} = {{E_{s} \cdot {\sum\limits_{k = 1}^{K}{{{{F(k)} \cdot {H(k)}} - 1}}^{2}}} + {N_{t} \cdot {\sum\limits_{k = 1}^{K}{{F(k)}}^{2}}} - {E_{s} \cdot {\sum\limits_{k = 1}^{K}{\lbrack {{{F(k)} \cdot {H(k)}} - 1} \rbrack \cdot {B^{*}(k)} \cdot {R( {k,k} )}}}} - {E_{s} \cdot {\overset{K}{\sum\limits_{k = 1}}{\lbrack {{{F(k)} \cdot {H(k)}} - 1} \rbrack^{*} \cdot {B(k)} \cdot {R^{*}( {k,k} )}}}} + {E_{s} \cdot {\sum\limits_{k = 1}^{K}{{B(k)}}^{2}}}}},} & {{Eq}\mspace{14mu} (15)}\end{matrix}$

where F(k), B(k) and R(k,k) are the k-th diagonal elements of K×Kmatrices F, B, and R, respectively. F(k) is the feed-forward filtercoefficient for frequency bin k, B(k) is the feedback filter coefficientfor bin k, and R(k,k) is a reliability value for bin k.

In an embodiment, the feed-forward and feedback filter responses arederived without any constraint on the feedback filter. For thisembodiment, the feedback filter impulse response may be given by L×1vector

=[b₀ b₁ b₂ . . . b_(L−1)]^(T). Vector

contains L time-domain filter taps b₀ through b_(L−1).

From equation (15), the feed-forward filter response may be given as:

$\begin{matrix}{{{F(k)} = \frac{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot {H^{*}(k)}}{{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot {{H(k)}}^{2}} + N_{t}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (16)}\end{matrix}$

The feedback filter response may be given as:

$\begin{matrix}{{{B(k)} = \frac{{- N_{t}} \cdot {R( {k,k} )}}{{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot {{H(k)}}^{2}} + N_{t}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (17)}\end{matrix}$

In equations (16) and (17), R(k,k) is indicative of the reliability ofthe feedback from the slicer.

In another embodiment, the feed-forward and feedback filter responsesare derived with a constraint of b₀=0 for the feedback filter. Thefeedback filter is typically used to compensate only for intersymbolinterference and hence there is no feedback related to the on-timesample. Coefficient b₀ determines the feedback for the on-time sampleand may be set to zero. For this embodiment, the feedback filter impulseresponse may be given by an L×1 vector

=[0 b₁ b₂ b_(L−1)]^(T).

The feedback filter response may be given as:

$\begin{matrix}{{\underset{\_}{b} = {{\underset{\_}{Q}}^{- 1} \cdot \underset{\_}{p}}},{and}} & {{Eq}\mspace{14mu} (18)} \\{{{B(k)} = {\sum\limits_{l = 1}^{L - 1}{b_{l} \cdot ^{{- j}\; 2{\pi \cdot {({k - 1})} \cdot {l/L}}}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,} & {{Eq}\mspace{14mu} (19)}\end{matrix}$

where Q is an (L−1)×(L−1) matrix and p is an (L−1)×1 vector.

The elements of Q may be given as:

$\begin{matrix}{{{Q( {m,l} )} = {\sum\limits_{k = 1}^{K}{( {\frac{{{R( {k,k} )}}^{2}}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}} + 1 - {{R( {k,k} )}}^{2}} ) \cdot ^{j\; 2{\pi \; \cdot {({k - 1})}}{{({m - l})}/K}}}}},} & {{Eq}\mspace{14mu} (20)}\end{matrix}$

where Q(m,l), for m,l=1, . . . , (L−1), is the element in row m andcolumn l of Q.

The elements of p may be given as:

$\begin{matrix}{{{p(m)} = {- {\sum\limits_{k = 1}^{K}{\frac{R( {k,k} )}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}} \cdot ^{j\; 2{\pi \cdot {({k - 1})}}{m/K}}}}}},} & {{Eq}\mspace{14mu} (21)}\end{matrix}$

where p(m), for m=1, (L−1), is the m-th element of p.

Vector

may be derived based on matrix Q and vector p, as shown in equation(18).

Vector

may then be transformed with an FFT/DFT to obtain the feedback filterresponse B(k), as shown in equation (19). To reduce computation, L maybe selected to be much less than K but large enough to cover significantISI components.

From equation (15) and with the constraint of b₀=0, the feed-forwardfilter response may be given as:

$\begin{matrix}{{{F(k)} = \frac{E_{s} \cdot \lbrack {1 + {{B(k)} \cdot {R^{*}( {k,k} )}}} \rbrack \cdot {H^{*}(k)}}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (22)}\end{matrix}$

Equation (22) indicates that the feed-forward filter response F(k) isdependent on the feedback filter response B(k) for the embodiment withb₀=0.

In yet another embodiment, the feed-forward and feedback filterresponses are derived with a constraint of b₀=0 for the feedback filterand with R(k,k)=ρ and L=K. ρ is a reliability factor for the feedbackand is not dependent on frequency.

For this embodiment, the feed-forward filter response may be given as:

$\begin{matrix}{{{F(k)} = \frac{E_{s} \cdot {H^{*}(k)} \cdot G_{F}}{{E_{s} \cdot {{H(k)}}^{2} \cdot ( {1 - \rho^{2}} )} + N_{t}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,} & {{Eq}\mspace{14mu} (23)}\end{matrix}$

where

$G_{F} = \frac{1}{1 + {\frac{E_{s} \cdot \rho^{2}}{K} \cdot {\sum\limits_{i = 1}^{K}\frac{{{H(i)}}^{2}}{{E_{s} \cdot {{H(i)}}^{2} \cdot ( {1 - \rho^{2}} )} + N_{t}}}}}$

is not dependent on frequency.

The feedback filter response may be given as:

$\begin{matrix}{\begin{matrix}{{{B(k)} = {( {{{F(k)} \cdot {H(k)}} - {\frac{1}{K} \cdot {\sum\limits_{i = 1}^{K}{{F(i)} \cdot {H(i)}}}}} ) \cdot \rho}},} \\{{= {\lbrack {{{F(k)} \cdot {H(k)}} - G_{B\;}} \rbrack \cdot \rho}},}\end{matrix}{{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,}} & {{Eq}\mspace{14mu} (24)}\end{matrix}$

where

$G_{B} = {\frac{1}{K} \cdot {\sum\limits_{i = 1}^{K}{{F(i)} \cdot {H(i)}}}}$

is also not dependent on frequency.

Equation (24) indicates that the feedback filter response B(k) isdependent on the feed-forward filter response F(k) for the embodimentwith b₀=0, R(k,k)=ρ, and L=K.

In yet another embodiment, the feed-forward and feedback filterresponses are derived with a constraint of b₀=0 for the feedback filterand with an assumption of no feedback errors so that ŝ(n)=s(n) andR(k,k)=1. For this embodiment, the feedback filter response may be givenas shown in equations (18) and (19), where

$\begin{matrix}{{{Q( {m,l} )} = {\sum\limits_{k = 1}^{K}\frac{^{j\; 2{\pi \cdot {({k - 1})}}{{({m - l})}/K}}}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}}}},{{for}\mspace{14mu} m},{l = 1},\ldots \mspace{14mu},( {L - 1} ),{and}} & {{Eq}\mspace{14mu} (25)} \\{{{p(m)} = {- {\sum\limits_{k = 1}^{K}\frac{^{j\; 2{\pi \cdot {({k - 1})}}{m/K}}}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}}}}},{{{for}\mspace{14mu} m} = 1},\ldots \mspace{14mu},{( {L - 1} ).}} & {{Eq}\mspace{14mu} (26)}\end{matrix}$

The feed-forward filter response may be given as:

$\begin{matrix}{{{F(k)} = \frac{E_{s} \cdot \lbrack {1 + {B(k)}} \rbrack \cdot {H^{*}(k)}}{{E_{s} \cdot {{H(k)}}^{2}} + N_{t}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (27)}\end{matrix}$

FIG. 4 shows an embodiment of a process 400 for deriving thefeed-forward and feedback filter responses and equalizing the inputsymbols. Initially, a channel impulse response h(n) is estimated andtransformed with an FFT/DFT to obtain a channel frequency response H(k)(block 412). A feedback correlation matrix R or a reliability factor ρis initialized, e.g., to zero for the first iteration (block 414). Forsome embodiments described above, matrix R may be equal to ρ·I, in whichcase R(k,k)=ρ, or may be equal to I, in which case R(k,k)=1.

A feed-forward filter response F(k) is derived based on the channelfrequency response H(k) and the feedback correlation R(k,k) or thereliability factor ρ (block 422). A feedback filter response B(k) isalso derived based on the channel frequency response H(k) and thefeedback correlation R(k,k) or the reliability factor ρ (block 424). Thefeed-forward and feedback filter responses may be derived without anyconstraint on the feedback filter, e.g., as shown in equations (16) and(17). The feed-forward and feedback filter responses may also be derivedwith a constraint of b₀=0 for the feedback filter, e.g., as shown inequations (18) through (22), or equations (23) and (24) for the casewith R(k,k)=ρ and L=K, or equations (25) through (27) for the case withR(k,k)=1. The chip estimates are not available for the first iteration.Hence, the derivation of the feedback filter response may be omitted forthe first iteration.

For some embodiments described above, matrix Q and vector p may bederived based on the channel frequency response H(k) and the feedbackcorrelation R(k,k) or the reliability factor ρ, e.g., as shown inequations (20) and (21) or equations (25) and (26).

The feedback filter response may then be derived based on matrix Q andvector p, e.g., as shown in equations (18) and (19).

In some embodiments, the feed-forward filter response and the feedbackfilter response may be derived independently of one another. In someother embodiments, the feed-forward filter response may be derivedfirst, and the feedback filter response may be derived with thefeed-forward filter response, e.g., as shown in equation (24). In yetsome other embodiments, the feedback filter response may be derivedfirst, and the feed-forward filter response may be derived with thefeed-forward filter response e.g., as shown in equation (22) or (27).

Equalization is performed on the input symbols R(k) based on thefeed-forward and feedback filter responses, e.g., as shown in equations(9) through (11) (block 426). The equalized symbols are transformed andsliced to obtain chip estimates ŝ(n) (block 428).

Equalization may be performed for one or multiple iterations. Eachiteration may also be called a stage, a round, and so on. Adetermination is made whether to perform another iteration (block 430).If the answer is ‘Yes’, then the feedback correlation matrix R or thereliability factor ρ is updated as described below (block 432). Matrix Ror reliability factor ρ should become larger for each iteration. Theprocess then returns to block 422 to update the feed-forward andfeedback filter responses and to perform equalization with the updatedfilter responses. Otherwise, if all iterations are completed and theanswer is ‘No’ for block 430, then the process terminates.

FIG. 5 shows an embodiment of a process 500 for performing decisionfeedback equalization. A channel estimate is obtained for acommunication channel (block 512). The channel estimate may be a channelimpulse response estimate, a channel frequency response estimate, and soon. A reliability parameter indicative of the reliability of thefeedback used for equalization is initialized (block 514). Thereliability parameter may be a feedback correlation matrix R, areliability factor ρ, and/or some other quantity. The reliabilityparameter may be a function of frequency or may be frequency invariant.

A feed-forward filter response is derived based on the channel estimateand the reliability parameter (block 522). A feedback filter response isderived based on the channel estimate and the reliability parameter(block 524). The feed-forward and feedback filter responses may bederived (1) without any constraint on the feedback filter, (2) with aconstraint of no feedback for an on-time sample, or (3) based on someother constraint or condition. The feed-forward and feedback filterresponses may be derived based on MMSE or some other criterion. Thefeed-forward and feedback filter responses may be derived independentlyof one another, the feedback filter response may be derived based on thefeed-forward filter response, or the feed-forward filter response may bederived based on the feedback filter response. The feed-forward filterresponse may be in the frequency domain and comprise frequency-domaincoefficients. The feedback filter response may be in (1) the frequencydomain and comprise frequency-domain coefficients or (2) the time domainand comprise time-domain taps. In general, different feed-forward andfeedback filter responses may be derived for different filterconstraints, assumptions on feedback reliability, design criteria, andso on.

Equalization is performed with the feed-forward and feedback filterresponses (block 526). The equalization may be performed on ablock-by-block basis for each received data block. Equalization may alsobe performed for multiple iterations. If another iteration is to beperformed, as determined in block 530, then the reliability parametermay be updated, and the feed-forward and feedback filter responses forthe next iteration may be derived based on the channel estimate and theupdated reliability parameter.

2. Fractionally-Spaced DFE

FIG. 6A shows a time-domain model 600 for a communication system withtwo times (2×) over-sampling at a receiver 650 a. A transmitter 610processes traffic data and generates transmit chips s(n′) at the chiprate, where n′ is an index for chip period. In an actual system,transmitter 610 sends the transmit chips via a communication channel 620to receiver 650 a. For model 600, an upsampler 612 inserts a zero aftereach transmit chip and provides output samples s(n) at the sample rate.Channel 620 is modeled with a channel impulse response of h(n) in block624 and additive noise of n(n) via a summer 626.

FIG. 6A also shows a fractionally-spaced DFE with a time-domain feedbackfilter. The term “fractionally-spaced” refers to sampling at a higherrate than the chip rate, and it is usually higher than the rate requiredby Nyquist sampling theorem. Receiver 650 a digitalizes the receivedsignal at twice the chip rate and obtains input samples r(n) at a samplerate that is twice the chip rate. A unit 652 transforms the inputsamples to the frequency domain with a 2K-point FFT/DFT and providesinput symbols R(k), for k=1, . . . , 2K. The 2× over-sampling of thereceived signal results in two copies of the signal spectrum beingavailable. The two redundant signal copies are referred to as a lowercopy (L) and an upper copy (U). The first K input symbols R(k), for k=1,. . . , K, are for the lower copy, are denoted as R_(L)(k), for k=1, . .. , K, and are provided to a feed-forward filter 660 a. The last K inputsymbols R(k), for k=K+1, . . . , 2K, are for the upper copy, are denotedas R_(U)(k), for k=1, . . . , K, and are provided to a feed-forwardfilter 660 b.

Feed-forward filter 660 a filters the input symbols R_(L)(k) andprovides filtered symbols X_(L)(k) for the lower copy. Feed-forwardfilter 660 b filters the input symbols R_(U)(k) and provides filteredsymbols X_(U)(k) for the upper copy. A summer 662 sums the filteredsymbols X_(L)(k) and X_(U)(k) on a bin-by-bin basis. A gain element 663scales the output of summer 662 with a gain of ½ and provides filteredsymbols X(k), for k=1, . . . , K. A unit 664 performs a K-pointIFFT/IDFT on the filtered symbols and provides filtered samples x(n) atthe chip rate. The summing of X_(L)(k) and X_(U)(k) by summer 662,scaling by ½ with unit 663, and K-point IFFT/IDFT by unit 664 isequivalent to performing a 2K-point IFFT/IDFT on X_(L)(k) and X_(U)(k)followed by decimation by a factor of two to obtain the filtered samplesx(n) at the chip rate. A summer 666 subtracts feedback samples y(n) fromthe filtered samples x(n) and provides equalized samples z(n). A slicer670 slices the equalized samples z(n) and provides chip estimates ŝ(n).A feedback filter 672 filters the chip estimates and provides thefeedback samples y(n).

FIG. 6B shows a block diagram of a model 602 with a fractionally-spacedDFE having a frequency-domain feedback filter. Transmitter 610 andchannel 620 are as described above for FIG. 6A. A receiver 650 b obtainsinput samples r(n) at the sample rate. Within receiver 650 b, FFT/DFTunit 652, feed-forward filters 660 a and 660 b, summer 662, and gainelement 663 operate on the input samples as described above for FIG. 6Aand provide filtered symbols X(k). Summer 666 subtracts feedback symbolsY(k) from the filtered symbols X(k) and provides equalized symbols Z(k).An IFFT/IDFT unit 668 transforms the equalized symbols to the timedomain and provides equalized samples z(n). Slicer 670 slices theequalized samples z(n) and provides chip estimates ŝ(n). An FFT/DFT unit674 transforms the chip estimates to the frequency domain and providessymbol estimates Ŝ(k). A feedback filter 680 filters the symbolestimates and provides the feedback symbols Y(k).

FIG. 7 shows a frequency-domain model 700 with a fractionally-spacedDFE. Model 700 is equivalent to model 600 in FIG. 6A and model 602 inFIG. 6B. A transmitter 710 generates time-domain transmit chips s(n′) atthe chip rate, which are sent via a communication channel 730. Forchannel 730, the time-domain transmit chips are transformed to thefrequency domain with a K-point FFT/DFT by a unit 732 to obtainfrequency-domain transmit symbols S(k), for k=1, . . . , K. The channelfor the lower signal copy is modeled by a frequency response of H_(L)(k)in block 734 a and additive noise of N_(L)(k) via a summer 736 a. Thechannel for the upper signal copy is modeled by a frequency response ofH_(U)(k) in block 734 b and additive noise of N_(U)(k) via a summer 736b. A unit 738 transforms the time-domain noise n(n) and provides thefrequency-domain noise N_(L)(k) and N_(U)(k) for the lower and uppercopies, respectively.

A receiver 750 obtains input symbols R_(L)(k) and R_(U)(k) for the lowerand upper copies, respectively. Feed-forward filters 760 a and 760 bfilter the input symbols R_(L)(k) and R_(U)(k) and provide filteredsymbols X_(L)(k) and X_(U)(k), respectively. The filtered symbolsX_(L)(k) and X_(U)(k) are summed by a summer 762 and scaled with a gainof ½ by a gain element 763 to obtain filtered symbols X(k). A summer 766subtracts feedback symbols Y(k) from the filtered symbols X(k) andprovides equalized symbols Z(k). The equalized symbols Z(k) aretransformed to the time domain by an IFFT/IDFT unit 768 and sliced by aslicer 770 to obtain chip estimates ŝ(n). The chip estimates aretransformed to the frequency domain by an FFT/DFT unit 774 and filteredby a feedback filter 780 to obtain the feedback symbols.

The input symbols may be expressed in matrix form for one data block, asfollows:

r _(L) =H _(L) ·s+n _(L), and

r _(U) =H _(U) ·s+n _(U),  Eq (28)

where

-   -   H _(L) is a K×K diagonal channel response matrix for the lower        copy,    -   H _(U) is a K×K diagonal channel response matrix for the upper        copy,    -   r _(L) is a K×1 vector of received symbols for the lower copy,    -   r _(U) is a K×1 vector of received symbols for the upper copy,        and    -   n _(L) and n _(U) are K×1 noise vectors for the lower and upper        copies, respectively.

The filtered symbols from feed-forward filters 760 a and 760 b may beexpressed as:

x _(L) =F _(L) ·r _(L), and

x _(U) =F _(U) ·r _(U),  Eq (29)

where F _(L) and F _(U) are K×K diagonal matrices for the feed-forwardfilter responses for the lower and upper copies, respectively, and

-   -   x _(L) and x _(U) are K×1 filtered symbol vectors for the lower        and upper copies.

The feedback symbols y from feedback filter 780 may be expressed as:

y=B·W _(K) ·{circumflex over (s)}.  Eq (30)

The equalized samples z provided to slicer 770 may be expressed as:

$\begin{matrix}\begin{matrix}{{\underset{\_}{z} = {{\underset{\_}{W}}_{K}^{- 1} \cdot \lbrack {{0.5 \cdot ( {{\underset{\_}{x}}_{L} + {\underset{\_}{x}}_{U}} )} - \underset{\_}{y}} \rbrack}},} \\{ {= {{\underset{\_}{W}}_{K}^{- 1} \cdot \lbrack {{0.5 \cdot ( {{{\underset{\_}{F}}_{L} \cdot {\underset{\_}{H}}_{L}} + {{\underset{\_}{F}}_{U} \cdot {\underset{\_}{H}}_{U}}} ) \cdot {\underset{\_}{W}}_{K} \cdot \underset{\_}{s}} - {\underset{\_}{B} \cdot {\underset{\_}{W}}_{k} \cdot \underset{\_}{\hat{s}}}} )}} \rbrack +} \\{{{0.5 \cdot {\underset{\_}{W}}_{K}^{- 1} \cdot \begin{bmatrix}{\underset{\_}{F}}_{L} & {\underset{\_}{F}}_{U}\end{bmatrix} \cdot {\underset{\_}{W}}_{2K} \cdot {\underset{\_}{n}}_{2K}},}}\end{matrix} & {{Eq}\mspace{14mu} (31)}\end{matrix}$

where W _(2K) is a 2K×2K Fourier matrix and n _(2K) is a 2K×1 noisevector. All other matrices in equation (31) are K×K matrices, and allother vectors are K×1 vectors.

The feed-forward filter frequency responses F _(L) and F _(U) and thefeedback filter frequency response B may be derived based on an MMSEcriterion that minimizes the MSE shown in equation (12) with theassumptions shown in equations (13) and (14). Equation (12) may beexpanded and combined with equations (13), (14) and (31). The MSE maythen be expressed as:

$\begin{matrix}{{{MSE} = {{E_{s} \cdot {\sum\limits_{k = 1}^{K}{{{0.5\lbrack {{{F_{L}(k)} \cdot {H_{L}(k)}} + {{F_{U}(k)} \cdot {H_{U}(k)}}} \rbrack} - 1}}^{2}}} + {0.5{N_{t} \cdot {\sum\limits_{k = 1}^{K}{{F_{L}(k)}}^{2}}}} + {{F_{U}(k)}}^{2} - {E_{s} \cdot {\sum\limits_{k = 1}^{K}{\{ {{0.5\lbrack {{{F_{L}(k)} \cdot {H_{L}(k)}} + {{F_{U}(k)} \cdot {H_{U}(k)}}} \rbrack} - 1} \} \cdot {B^{*}(k)} \cdot {R( {k,k} )}}}} - {E_{s} \cdot {\sum\limits_{k = 1}^{K}{\{ {{0.5\lbrack {{{F_{L}(k)} \cdot {H_{L}(k)}} + {{F_{U}(k)} \cdot {H_{U}(k)}}} \rbrack} - 1} \}^{*} \cdot {B(k)} \cdot {R^{*}( {k,k} )}}}} + {E_{s} \cdot {\sum\limits_{k = 1}^{K}{{B(k)}}^{2}}}}},} & {{Eq}\mspace{14mu} (32)}\end{matrix}$

where F_(L)(k), F_(U)(k), H_(L)(k), H_(U)(k) are the k-th diagonalelements of K×K matrices F _(L), F _(U), H _(L) and H _(U),respectively.

In an embodiment, the feed-forward and feedback filter responses arederived without any constraint on the feedback filter. For thisembodiment, the feedback filter impulse response may be given by L×1vector

=[b₀ b₂ . . . b_(L−1)]^(T).

From equation (32), the feed-forward filter response may be given as:

$\begin{matrix}{{{F_{c}(k)} = \frac{2{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot {H_{c}^{*}(k)}}}{{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,} & {{Eq}\mspace{14mu} (33)}\end{matrix}$

where H_(c)(k), for c=L, U, is the channel gain for frequency bin k incopy c, and

-   -   F_(c)(k), for c=L, U, is the feed-forward filter coefficient for        bin k in copy c.

The feedback filter response may be given as:

$\begin{matrix}{{{B(k)} = \frac{{- 2}{N_{t} \cdot {R( {k,k} )}}}{{E_{s} \cdot ( {1 - {{R( {k,k} )}}^{2}} ) \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (34)}\end{matrix}$

In another embodiment, the feed-forward and feedback filter responsesare derived with a constraint of b₀=0 for the feedback filter. For thisembodiment, the feedback filter impulse response may be given by L×1vector

=[0 b₁ b₂ . . . b_(L−1)]^(T). To reduce computation, L may be selectedto be much less than K but large enough to cover significant ISIcomponents.

The feedback filter response may be given as shown in equations (18) and(19), where the elements of matrix Q, for m,l=1, . . . , (L−1), may begiven as:

$\begin{matrix}{{Q( {m,l} )} = {\sum\limits_{k = 1}^{K}{( {\frac{2{N_{t} \cdot {{R( {k,k} )}}^{2}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}} + 1 - {{R( {k,k} )}}^{2}} ) \cdot {^{j\; 2{\pi \cdot {({k - 1})}}{{({m - l})}/K}}.}}}} & {{Eq}\mspace{14mu} (35)}\end{matrix}$

The elements of vector p, for m=1, . . . , (L−1), may be given as:

$\begin{matrix}{{p(m)} = {- {\sum\limits_{k = 1}^{K}{\frac{2{N_{t} \cdot {R( {k,k} )}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}} \cdot {^{j\; 2{\pi \cdot {({k - 1})}}{m/K}}.}}}}} & {{Eq}\mspace{14mu} (36)}\end{matrix}$

From equation (32) and with the constraint of b₀=0, the feed-forwardfilter responses may be given as:

$\begin{matrix}{{{F_{c}(k)} = \frac{2{E_{s} \cdot \lbrack {1 + {{B(k)} \cdot {R^{*}( {k,k} )}}} \rbrack \cdot {H_{c}^{*}(k)}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (37)}\end{matrix}$

In yet another embodiment, the feed-forward and feedback filterresponses are derived with a constraint of b₀=0 for the feedback filterand with R(k,k)=ρ and L=K. For this embodiment, the feed-forward filterresponse may be given as:

$\begin{matrix}{{{{F_{c}(k)} = \frac{2{E_{s} \cdot {H_{c}^{*}(k)} \cdot G_{F\; 2}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} ) \cdot ( {1 - \rho^{2}} )} + {2N_{t}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,{where}}{G_{F\; 2} = {\frac{1}{1 + {\frac{E_{s} \cdot \rho^{2}}{K} \cdot {\sum\limits_{i = 1}^{K}\frac{( {{{H_{L}(i)}}^{2} + {{H_{U}(i)}}^{2}} )}{\begin{matrix}{E_{s} \cdot ( {{{H_{L}(i)}}^{2} + {{H_{U}(i)}}^{2}} ) \cdot} \\{( {1 - \rho^{2}} ) + {2N_{t}}}\end{matrix}}}}}.}}} & {{Eq}\mspace{14mu} (38)}\end{matrix}$

The feedback filter response may be given as:

$\begin{matrix}{{{{B(k)} = {\{ {{0.5\lbrack {{{F_{L}(k)} \cdot {H_{L}(k)}} + {{F_{U}(k)} \cdot {H_{U}(k)}}} \rbrack} - G_{B\; 2}} \} \cdot \rho}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},K,{where}}{G_{B\; 2} = {\frac{1}{2K} \cdot {\sum\limits_{i = 1}^{K}{\lbrack {{{F_{L}(i)} \cdot {H_{L}(i)}} + {{F_{U}(i)} \cdot {H_{U}(i)}}} \rbrack.}}}}} & {{Eq}\mspace{14mu} (39)}\end{matrix}$

In yet another embodiment, the feed-forward and feedback filterresponses are derived with a constraint of b₀=0 for the feedback filterand with an assumption of no feedback errors so that ŝ(n)=s(n) andR(k,k)=1. For this embodiment, the feedback filter response may be givenas shown in equations (18) and (19), where

$\begin{matrix}{{{Q( {m,l} )} = {\sum\limits_{k = 1}^{K}\frac{^{j\; 2{\pi \cdot {({k - 1})}}{{({m - l})}/k}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}}}},{{for}\mspace{14mu} m},{l = 1},\ldots \mspace{14mu},( {L - 1} ),{and}} & {{Eq}\mspace{14mu} (40)} \\{{{p(m)} = {- {\sum\limits_{k = 1}^{K}\frac{^{j\; 2{\pi \cdot {({k - 1})}}{m/K}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t}}}}}},{{{for}\mspace{14mu} m} = 1},\ldots \mspace{14mu},{( {L - 1} ).}} & {{Eq}\mspace{14mu} (41)}\end{matrix}$

The feed-forward filter responses may be given as:

$\begin{matrix}{{{F_{c}(k)} = \frac{2{E_{s} \cdot \lbrack {1 + {B(k)}} \rbrack \cdot {H_{c}^{*}(k)}}}{{E_{s} \cdot ( {{{H_{L}(k)}}^{2} + {{H_{U}(k)}}^{2}} )} + {2N_{t\;}}}},{{{for}\mspace{14mu} k} = 1},\ldots \mspace{14mu},{K.}} & {{Eq}\mspace{14mu} (42)}\end{matrix}$

FIG. 8 shows an embodiment of a process 800 for derivingfractionally-spaced feed-forward and feedback filter responses andequalizing the input symbols. Initially, a channel impulse response h(n)is estimated and transformed with an FFT/DFT to obtain channel frequencyresponses H_(L)(k) and H_(U)(k) for the lower and upper signal copies,respectively (block 812). A feedback correlation matrix R or areliability factor ρ is initialized, e.g., to zero(s) for the firstiteration (block 814).

Feed-forward filter responses F_(L)(k) and F_(U)(k) for the lower andupper copies are derived based on the channel frequency responsesH_(L)(k) and H_(U)(k) and the feedback correlation R(k,k) or thereliability factor ρ, e.g., as shown in equation (33), (37), (38) or(42) (block 822). A feedback filter response B(k) is also derived basedon the channel frequency responses H_(L)(k) and H_(U)(k) and thefeedback correlation R(k,k) or the reliability factor ρ, e.g., as shownin equation (34), (35) and (36), (39), or (40) and (41) (block 824).Equalization is performed on the input symbols R_(L)(k) and R_(U)(k) forthe lower and upper copies based on the feed-forward and feedback filterresponses, e.g., as shown in equations (29) through (31) (block 826).The equalized symbols are transformed and sliced to obtain chipestimates ŝ(n) (block 828).

Equalization may be performed for one or multiple iterations. Adetermination is made whether to perform another iteration (block 830).If the answer is ‘Yes’, then the feedback correlation matrix R or thereliability factor ρ is updated (block 832). The process then returns toblock 822 to update the feed-forward and feedback filter responses andto perform equalization with the updated filter responses. Otherwise, ifall iterations are completed and the answer is ‘No’ for block 830, thenthe process terminates.

For clarity, the fractionally-spaced DFE has been described for 2×over-sampling at the receiver, or C=2, where C is the over-samplingratio. In general, the fractionally-spaced DFE may be used with anyamount of over-sampling. In the equations above, the term(|H_(L)(k)|²+|H_(U)(k)|²) may be substituted with (|H₁(k)|²+ . . .+|H_(C) (k)|²), index c may run from 1 through C, and the factor of 2may be substituted with C where appropriate.

For clarity, the chip-spaced DFE and fractionally-spaced DFE have beendescribed for a single receive antenna at the receiver. The DFEsdescribed herein may also be used for a receiver with multiple (R)antennas, which may be employed for receive diversity or amultiple-input multiple-output (MIMO) transmission. For chip ratesampling with receive diversity, the receiver obtains R signal copiesand R channel frequency responses for the R receive antennas. Thereceiver may derive R feed-forward filter responses for the R signalcopies, e.g., based on the description above for the fractionally-spacedDFE, albeit with the signal copies being from different receive antennasinstead of different parts of the signal spectrum. For over-samplingwith receive diversity, the receiver obtains R·C signal copies and R·Cchannel frequency responses for the R receive antennas and C timesover-sampling. The receiver may derive R·C feed-forward filter responsesfor the R·C signal copies, e.g., based on the description above for thefractionally-spaced DFE, albeit with the signal copies being fromdifferent receive antennas as well as different parts of the signalspectrum.

FIG. 9 shows an embodiment of a process 900 for performing decisionfeedback equalization for multiple signal copies, which may be obtainedvia multiple receive antennas and/or over-sampling. Channel estimatesare obtained for the multiple signal copies (block 912). The channelestimates may be channel impulse response estimates, channel frequencyresponse estimates, and so on. A reliability parameter, which may be afeedback correlation matrix R, a reliability factor ρ, and/or some otherquantity, is initialized (block 914).

Feed-forward filter responses for the multiple signal copies are derivedbased on the channel estimates and the reliability parameter (block922). A feedback filter response is derived based on the channelestimates and the reliability parameter (block 924). The feed-forwardand feedback filter responses may be derived (1) without any constrainton the feedback filter, (2) with a constraint of no feedback for anon-time sample, or (3) based on some other constraint or condition. Thefeed-forward and feedback filter responses may be derived based on MMSEor some other criterion. The feed-forward and feedback filter responsesmay be derived independently, the feedback filter response may bederived based on the feed-forward filter responses, or the feed-forwardfilter responses may be derived based on the feedback filter response.In general, different feed-forward and feedback filter responses may bederived for different filter constraints, assumptions on feedbackreliability, design criteria, and so on.

Equalization is performed with the feed-forward and feedback filterresponses (block 926). The equalization may be performed on ablock-by-block basis for each received data block. Equalization may alsobe performed for multiple iterations. If another iteration is to beperformed, as determined in block 930, then the reliability parametermay be updated in block 932, and the feed-forward and feedback filterresponses for the next iteration may be derived based on the channelestimates and the updated reliability parameter.

3. Decision Feedback Reliability

The feed-forward and feedback filter responses may be derived based onR(k,k) or p, which is related to the reliability of the chip estimatess(n). The chip estimates are tentative decisions that are fed back forequalization. The amount of feedback is related to how reliable the chipestimates are statistically. The amount of feedback may be large if thechip estimates are very reliable and may be small if the chip estimatesare not too reliable. In the extreme case, there may be no feedback ifthe chip estimates are completely unreliable.

The reliability of the chip estimates may be estimated in variousmanners. In an embodiment, the reliability is estimated based oncorrectly decoded blocks. An error detection code, such as a cyclicredundancy check (CRC) code, may be used to determine whether a givenblock is decoded correctly. The transmitter may generate a CRC for adata block and append the CRC as part of the data block. The receivermay use the appended CRC for error detection. After decoding the block,the receiver may generate a CRC based on the decoded block and maycompare the generated CRC against the appended CRC. If the two CRCsmatch, then the block is deemed to have been decoded correctly, and allof the chips in that block become known to the receiver.

The receiver may use a correctly decoded block to compute thereliability of the chip estimates at various stages or iterations ofequalization. The receiver may process the decoded block in the samemanner performed by the transmitter and regenerate the transmit chipss(n) sent by the transmitter for the data block. In an embodiment, thereceiver may correlate the transmit chips s(n) with the chip estimatesŝ_(i)(n) for a given stage i to obtain a reliability factor ρ_(i) forthat stage, as follows:

$\begin{matrix}{\rho_{i} = {\frac{1}{E_{s} \cdot K} \cdot {{{\sum\limits_{k = 1}^{K}{{s(n)} \cdot {{\hat{s}}_{i}^{*}(n)}}}}.}}} & {{Eq}\mspace{14mu} (43)}\end{matrix}$

In another embodiment, the receiver may derive a feedback correlationmatrix R _(i) for stage i, as follows:

$\begin{matrix}{{{\underset{\_}{R}}_{i} = {\frac{1}{E_{s}} \cdot \underset{\_}{s} \cdot {\underset{\_}{\hat{s}}}_{i}^{H}}},} & {{Eq}\mspace{14mu} (44)}\end{matrix}$

where {circumflex over (s)}_(i) is a K×1 vector of symbol estimates forstage i.

Different chip estimates are obtained and fed back for equalization indifferent stages. Hence, the receiver may estimate the feedbackreliability for different stages based on the chip estimates for thesestages.

The reliability of the decision feedback may be filtered across multiplecorrectly decoded blocks to reduce variation. The filtering may beperformed based on a finite impulse response (FIR) filter, an infiniteimpulse response (IIR) filter, or some other type of filter. The timeconstant or bandwidth for the filter may be selected based on theexpected rate of change in the channel conditions. A large time constantor small bandwidth may be used for a slowly varying channel. Conversely,a small time constant or large bandwidth may be used for a fast changingchannel. The time constant of the filter may be adaptive based onDoppler for the receiver.

Adjacent data blocks may be assumed to have appropriately similardecision feedback reliability for the same stage of equalization. Inthis case, the reliability estimated for different stages based oncorrectly decoded blocks may be used for decision-feedback equalizationof future blocks.

The reliability of the decision feedback may be dependent on themodulation scheme used by the transmitter. In an embodiment, feedbackreliability is estimated and maintained for different modulationschemes. For this embodiment, the reliability estimated for correctlydecoded blocks sent with a given modulation scheme is used forequalization of future blocks sent with the same modulation scheme. Inanother embodiment, the feedback reliability is estimated in a manner toaccount for different modulation schemes used for the correctly decodedblocks.

The reliability of the decision feedback may also be estimated based onother transmissions that are known a priori or ascertained by thereceiver. For example, if a data block includes a known portion (e.g., aunique word, a preamble, and/or some other known information), then thefeedback reliability may be estimated based on this known portion.

The receiver may use the estimated feedback reliability to derive thefeed-forward and feedback filter responses. The receiver may also usethe feedback reliability to determine whether to perform decisionfeedback equalization or linear equalization (without decisionfeedback). For example, the receiver may perform linear equalization ifthe feedback is too unreliable.

FIG. 10 shows an embodiment of a process 1000 for performing decisionfeedback equalization based on a reliability parameter derived fromcorrectly decoded blocks. The reliability parameter is estimated basedon a first data block that is decoded correctly, which may be determinedbased on a CRC or some other error detection code (block 1012). Thereliability parameter may be estimated based on (1) correlation of thetransmit chips with the chip estimates, e.g., as shown in equation (43),or (2) an outer product of the transmit symbols and the symbolestimates, e.g., as shown in equation (44). The reliability parametermay be filtered across multiple correctly decoded blocks. The timeconstant for the filtering may be selected based on channel conditionsand/or other factors.

A feed-forward filter response and a feedback filter response arederived based on a channel estimate and the reliability parameter (block1014). Equalization is performed for a second data block with thefeed-forward and feedback filter responses (block 1016). If equalizationis performed in multiple iterations or stages, then the reliabilityparameter may be estimated for each stage based on the first data blockand the chip or symbol estimates for that stage. The feed-forward andfeedback filter responses for each iteration may be derived based on thereliability parameter for that iteration.

FIG. 11 shows a block diagram of an embodiment of a transmitter 1110 anda receiver 1150 in a communication system 1100. For a downlink/forwardlink transmission, transmitter 1110 is part of a base station, andreceiver 1150 is part of a wireless device. For an uplink/reverse linktransmission, transmitter 1110 is part of a wireless device, andreceiver 1150 is part of a base station. A base station is typically afixed station that communicates with the wireless devices and may alsobe called a Node B, an access point, and so on. A wireless device may befixed or mobile and may also be called a user equipment (UE), a mobilestation, a user terminal, a subscriber unit, and so on. A wirelessdevice may be a cellular phone, a personal digital assistant (PDA), awireless modem card, or some other device or apparatus.

At transmitter 1110, a transmit (TX) data processor 1120 processes(e.g., encodes, interleaves, and symbol maps) traffic data and generatesdata symbols. As used herein, a data symbol is a modulation symbol fordata, a pilot symbol is a modulation symbol for pilot, a modulationsymbol is a complex value for a point in a signal constellation (e.g.,for M-PSK or M-QAM), and pilot is data that is known a priori by boththe transmitter and receiver. A modulator 1130 process the data symbolsand pilot symbols in a manner specified by the system and providestransmit chips s(n) to a transmitter unit (TMTR) 1132. Transmitter unit1132 processes (e.g., converts to analog, amplifies, filters, andfrequency upconverts) the transmit chips and generates an RF signal,which is transmitted from an antenna 1134.

At receiver 1150, an antenna 1152 receives the transmitted RF signal viavarious signal paths and provides a received signal to a receiver unit(RCVR) 1154. Receiver unit 1154 conditions (e.g., filters, amplifies,and frequency downconverts) the received signal, digitizes theconditioned signal at a sample rate that may be equal to or higher thanthe chip rate, and provides time-domain input samples. An FFT/DFT unit1156 transforms the input samples to the frequency domain and providesfrequency-domain input symbols.

A channel and noise estimator 1158 estimates the channel response andthe noise based on the frequency-domain input symbols and/or thetime-domain input samples. A decision feedback equalizer (DFE) 1160derives the feed-forward filter response(s) and the feedback filterresponse based on the channel and noise estimates and a reliabilityparameter. The reliability parameter may be estimated and updated by DFE1160, a controller 1190, or some other unit based on correctly decodedblocks and/or other known transmissions.

DFE 1160 filters the input symbols based on the feed-forward andfeedback filter responses and provides chip estimates to a demodulator(Demod) 1170. DFE 1160 may implement any of the DFE designs describedabove. Demodulator 1170 processes the chip estimates in a mannercomplementary to the processing by modulator 1130 and provides datasymbol estimates. A receive (RX) data processor 1180 processes (e.g.,symbol demaps, deinterleaves, and decodes) the data symbol estimates andprovides decoded data. RX data processor 1180 may also check each datablock based on the CRC. In general, the processing by demodulator 1170and RX data processor 1180 is complementary to the processing bymodulator 1130 and TX data processor 1120, respectively, at transmitter1110.

Controllers/processors 1140 and 1190 direct operation of variousprocessing units at transmitter 1110 and receiver 1150, respectively.Memories 1142 and 1192 store data and program codes for transmitter 1110and receiver 1150, respectively.

The equalization techniques described herein may be used for variouscommunication systems such as Code Division Multiple Access (CDMA)systems, Time Division Multiple Access (TDMA) systems, FrequencyDivision Multiple Access (FDMA) systems, Orthogonal FDMA (OFDMA)systems, Single-Carrier FDMA (SC-FDMA) systems, and so on. A CDMA systemmay implement one or more radio technologies such as Wideband-CDMA(W-CDMA), cdma2000, and so on. cdma2000 covers IS-2000, IS-856, andIS-95 standards. A TDMA system may implement a radio technology such asGlobal System for Mobile Communications (GSM). These various radiotechnologies and standards are known in the art. An OFDMA systemtransmits modulation symbols in the frequency domain on orthogonalsubcarriers using orthogonal frequency division multiplexing (OFDM). AnSC-FDMA system transmits modulation symbols in the time domain onorthogonal subcarriers.

Modulator 1130 at transmitter 1110 and demodulator 1170 at receiver 1150perform processing as specified by the system. For example, modulator1130 may perform processing for CDMA, OFDM, SC-FDMA, and so on, or acombination thereof.

Those of skill in the art would understand that information and signalsmay be represented using any of a variety of different technologies andtechniques. For example, data, instructions, commands, information,signals, bits, symbols, and chips that may be referenced throughout theabove description may be represented by voltages, currents,electromagnetic waves, magnetic fields or particles, optical fields orparticles, or any combination thereof.

Those of skill would further appreciate that the various illustrativelogical blocks, modules, circuits, and algorithm steps described inconnection with the embodiments disclosed herein may be implemented aselectronic hardware, computer software, or combinations of both. Toclearly illustrate this interchangeability of hardware and software,various illustrative components, blocks, modules, circuits, and stepshave been described above generally in terms of their functionality.Whether such functionality is implemented as hardware or softwaredepends upon the particular application and design constraints imposedon the overall system. Skilled artisans may implement the describedfunctionality in varying ways for each particular application, but suchimplementation decisions should not be interpreted as causing adeparture from the scope of the present invention.

The various illustrative logical blocks, modules, and circuits describedin connection with the embodiments disclosed herein may be implementedor performed with a general purpose processor, a digital signalprocessor (DSP), an application specific integrated circuit (ASIC), afield programmable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

The steps of a method or algorithm described in connection with theembodiments disclosed herein may be embodied directly in hardware, in asoftware module executed by a processor, or in a combination of the two.A software module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. Anexemplary storage medium is coupled to the processor such that theprocessor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor. The processor and the storage medium may reside in anASIC. The ASIC may reside in a user terminal. In the alternative, theprocessor and the storage medium may reside as discrete components in auser terminal.

Headings are included herein for reference and to aid in locatingcertain sections. These headings are not intended to limit the scope ofthe concepts described therein under, and these concepts may haveapplicability in other sections throughout the entire specification.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. A method comprising: deriving (424, 524), in the frequency domain, afeed-forward filter response and a feedback filter response based on achannel estimate and a reliability parameter wherein the step ofderiving comprises: in an initial iteration, initializing a feedbackcorrelation matrix or a reliability factor to zero(s); and performing(426, 526) equalization with the feed-forward and feedback filterresponses.
 2. The method of claim 1, further comprising: estimating(1012) the reliability parameter based on a data block that is decodedcorrectly.
 3. The method of claim 1, wherein equalization is performedfor multiple iterations, and wherein the deriving the feed-forward andfeedback filter responses comprises updating (432, 532) the reliabilityparameter for each iteration, and deriving the feed-forward and feedbackfilter responses for each iteration based on the channel estimate andthe reliability parameter for the iteration.
 4. A method of claim 1comprising: deriving (822, 922) multiple feed-forward filter responsesfor multiple signal copies based on channel estimates for the multiplesignal copies and a reliability parameter; deriving (824, 924) afeedback filter response based on the channel estimates and thereliability parameter; and performing (826, 926) equalization on inputsymbols for the multiple signal copies with the multiple feed-forwardfilter responses and the feedback filter response.
 5. The method ofclaim 4, wherein the deriving the multiple feed-forward filter responsescomprises deriving the multiple feed-forward filter responses withoutconstraint on the feedback filter response, and wherein the deriving thefeedback filter response comprises deriving the feedback filter responsewithout constraint on the feedback filter response.
 6. The method ofclaim 4, wherein the deriving the multiple feed-forward filter responsescomprises deriving the multiple feed-forward filter responses with aconstraint of no feedback for an on-time sample, and wherein thederiving the feedback filter response comprises deriving the feedbackfilter response with the constraint of no feedback for the on-timesample.
 7. A method of claim 1 comprising: estimating (1012) areliability parameter based on a first data block that is decodedcorrectly; deriving (1014) a feed-forward filter response and a feedbackfilter response based on a channel estimate and the reliabilityparameter; and performing equalization (1016) for a second data blockwith the feed-forward and feedback filter responses.
 8. The method ofclaim 7, wherein the estimating the reliability parameter comprisesgenerating transmit chips based on the first data block, and estimatingthe reliability parameter based on correlation between the transmitchips and chip estimates from the equalization.
 9. The method of claim7, wherein the estimating the reliability parameter comprises estimatingthe reliability parameter for each of multiple iterations ofequalization based on the first data block, wherein the deriving thefeed-forward and feedback filter responses comprises deriving thefeed-forward and feedback filter responses for each iteration based onthe reliability parameter for the iteration, and wherein the performingequalization comprises performing each iteration of equalization for thesecond data block with the feed-forward and feedback filter responsesfor the iteration.
 10. The method of claim 1, wherein the step ofderiving further comprises in a subsequent iteration, constraining thefeedback filter response to no feedback for an on-time sample.
 11. Anapparatus comprising: means for deriving (422, 522), in the frequencydomain, a feed-forward filter response and a feedback filter responsebased on a channel estimate and a reliability parameter, means forinitializing, in an initial iteration, a feedback correlation matrix ora reliability factor to zero(s); and means for performing (426, 526)equalization with the feed-forward and feedback filter responses. 12.The apparatus of claim 11, further comprising: means for estimating(1012) the reliability parameter based on a data block that is decodedcorrectly.
 13. The apparatus of claim 11, wherein equalization isperformed for multiple iterations, and wherein the means for derivingthe feed-forward and feedback filter responses comprises means forupdating (432, 532) the reliability parameter for each iteration, andmeans for deriving the feed-forward and feedback filter responses foreach iteration based on the channel estimate and the reliabilityparameter for the iteration.
 14. The apparatus of claim 11 furthercomprises means for providing feedback, in a subsequent iteration with aconstraint of no feedback for an on-time sample.
 15. An apparatus ofclaim 11 comprising: at least one processor to derive (822, 922)multiple feed-forward filter responses for multiple signal copies basedon channel estimates for the multiple signal copies and a reliabilityparameter, to derive (824, 924) a feedback filter response based on thechannel estimates and the reliability parameter, and to performequalization on input symbols for the multiple signal copies with themultiple feed-forward filter responses and the feedback filter response;and a memory coupled to the at least one processor.
 16. The apparatus ofclaim 14, wherein the at least one processor is operable to derive thefeed-forward and feedback filter responses without constraint on thefeedback filter response.
 17. The apparatus of claim 14, wherein the atleast one processor is derives the feed-forward and feedback filterresponses with a constraint of no feedback for an on-time sample. 18.The apparatus of claim 14, wherein the at least one processor isoperable to obtain the multiple signal copies via over-sampling of areceived signal.
 19. The apparatus of claim 14, wherein the at least oneprocessor is operable to obtain the multiple signal copies via multiplereceive antennas.
 20. The apparatus of claim 14, wherein the at leastone processor is operable to obtain the multiple signal copies viamultiple receive antennas and over-sampling of a received signal fromeach receive antenna.
 21. An apparatus of claim 11 comprising: means forderiving (822, 922) multiple feed-forward filter responses for multiplesignal copies based on channel estimates for the multiple signal copiesand a reliability parameter; means for deriving (824, 924) a feedbackfilter response based on the channel estimates and the reliabilityparameter; and means for performing (826, 926) equalization on inputsymbols for the multiple signal copies with the multiple feed-forwardfilter responses and the feedback filter response.
 22. The apparatus ofclaim 21, wherein the means for deriving the multiple feed-forwardfilter responses comprises means for deriving the multiple feed-forwardfilter responses without constraint on the feedback filter response, andwherein the means for deriving the feedback filter response comprisesmeans for deriving the feedback filter response without constraint onthe feedback filter response.
 23. The apparatus of claim 21, wherein themeans for deriving the multiple feed-forward filter responses comprisesmeans for deriving the multiple feed-forward filter responses with aconstraint of no feedback for an on-time sample, and wherein the meansfor deriving the feedback filter response comprises means for derivingthe feedback filter response with the constraint of no feedback for theon-time sample.
 24. An apparatus of claim 11 comprising: at least oneprocessor to estimate (1012) a reliability parameter based on a firstdata block that is decoded correctly, to derive (1014) a feed-forwardfilter response and a feedback filter response based on a channelestimate and the reliability parameter, and to perform equalization(1016) for a second data block with the feed-forward and feedback filterresponses; and a memory operatively coupled to the at least oneprocessor.
 25. The apparatus of claim 24, wherein the at least oneprocessor is operable to determine that the first data block is decodedcorrectly based on a cyclic redundancy check (CRC).
 26. The apparatus ofclaim 24, wherein the at least one processor is operable to generatetransmit chips based on the first data block and estimates thereliability parameter based on correlation between the transmit chipsand chip estimates from the equalization.
 27. The apparatus of claim 24,wherein the at least one processor is operable to generate transmitsymbols based on the first data block and estimates the reliabilityparameter based on an outer product of the transmit symbols and symbolestimates from the equalization.
 28. The apparatus of claim 24, whereinthe at least one processor is operable to estimate the reliabilityparameter for each of multiple iterations of equalization based on thefirst data block, derives the feed-forward and feedback filter responsesfor each iteration based on the reliability parameter for the iteration,and performs each iteration of equalization for the second data blockwith the feed-forward and feedback filter responses for the iteration.29. The apparatus of claim 24, wherein the at least one processor isoperable to filter the reliability parameter across multiple correctlydecoded data blocks.
 30. The apparatus of claim 24, wherein the at leastone processor is operable to select a time constant based on channelconditions and filters the reliability parameter across multiplecorrectly decoded data blocks in accordance with the selected timeconstant.
 31. The apparatus of claim 24, wherein the at least oneprocessor is operable to determine whether or not to derive and use thefeedback filter response based on the reliability parameter.
 32. Anapparatus of claim 24 comprising: means for estimating (1012) areliability parameter based on a first data block that is decodedcorrectly; means for deriving (1014) a feed-forward filter response anda feedback filter response based on a channel estimate and thereliability parameter; and means for performing equalization (1016) fora second data block with the feed-forward and feedback filter responses.33. The apparatus of claim 32, wherein the means for estimating thereliability parameter comprises means for generating transmit chipsbased on the first data block, and means for estimating the reliabilityparameter based on correlation between the transmit chips and chipestimates from the equalization.
 34. The apparatus of claim 32, whereinthe means for estimating the reliability parameter comprises means forestimating the reliability parameter for each of multiple iterations ofequalization based on the first data block, wherein the means forderiving the feed-forward and feedback filter responses comprises meansfor deriving the feed-forward and feedback filter responses for eachiteration based on the reliability parameter for the iteration, andwherein the means for performing equalization comprises means forperforming each iteration of equalization for the second data block withthe feed-forward and feedback filter responses for the iteration. 35.The apparatus of claim 11, wherein the reliability parameter is afunction of frequency.
 36. The apparatus of claim 11, wherein thereliability parameter is frequency invariant.